This is neatly defined polyline function. However, as the spline parameter goes from 0 to 1 with some constant step, calculated points are somewhere denser than at other regions. (I can see the density decreases with distance between points.)

Graphics[{
Point[p], Opacity[.2],
Point[f /@ Range[0, 1, .001]]}]

Me I need a function that returns equidistant points for equidistant parameter values.

This can be made more elegantly, right, with Mathematica? With some option that samples equidistant points? Because say I have some smooth curve function. I don't know how I would tackle this then. I guess one would have to integrate and findroot some.

Basic-calculus approach, clean and tiny. Thank you. The jumping around the original point parameter values isn't noticeable in my animation -- and I can decrease the step size which diminishes the jumping, and then Take only every second, third or so point since there are probably too many for my purpose.
–
BoLeMar 25 '13 at 12:57

@BoLe Yep. The idea was to keep it simple :)
–
belisariusMar 25 '13 at 14:04

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